MATT: Okay, so we're going to look at a sequence of numbers,
and it's not going to be this one, which is where I start with a 1,
and then, for no obviously explained reason, another 1,
and then I feel the need to add them together,
which gives me a 2.
If I add the last two terms together, I get a 3.
If I add those together, I get a 5, I get an 8, and so on,
and most people will recognize these as our friends, the Fibonacci numbers,
and they're famous for a number of reasons.
In fact,— Oh, well, Brady,
do you know why, why people get so excited about these numbers?
I mean, you've talked to many people, I imagine, over the years.
BRADY: It's because of sunflowers
MATT: Because of sunflowers, yes,
or pineapples, or petals
and, so yes, often things in nature
occur in numbers, and some of those numbers
are in this list.
The other big one,
and people almost take Fibonacci to be synonymous with this,
is the golden ratio,
and people will switch between saying "Fibonacci numbers"/"golden ratio"
and I think it's time we stop doing that.
I'm here to tell you that the Fibonacci numbers are terrible,
and they have very little to do with the golden ratio.
In fact, there's a much better sequence of numbers
which we should use instead of Fibonacci
when it comes to the golden ratio.
But first, we'll establish what we're making fun of before we tear it apart.
So the reason we like Fibonacci numbers linking to the golden ratio
so if you take the ratio of two of the terms,
so the last one here I've got is 34,
take the ratio of 34 with 21,
so if I do 34 divided by 21
it equals 1.6190…, so it's close.
And so these terms approach the ratio of the golden ratio.
If I kept writing these numbers,
If I carried on, and, you know, let's—
I don't know how much space you've got on your camera,
if we did this for two, maybe three years,
the numbers would be closer and closer to the golden ratio,
and the limit they're approaching is the golden ratio.
They'll never reach it, but if you do it for infinitely many terms
in the Fibonacci sequence,
the ratio is the golden ratio.
It is a lovely link.
The trouble is the Fibonacci sequence is not the only one that does this.
So, in fact, we're going to try another one entirely at random.
So can you give me, Brady, instead of starting 1, 1,…
can you give me a number in the thousands, four digits,
What would you like?
BRADY: Uh, 2308.
MATT: 2308, and another number.
BRADY: 4261
MATT: Okay, so there's our two random numbers.
You got 2308, and you got 4261.
So instead of starting 1, 1, and adding those to get 2,
I'm going to start 2308, second term will be 4261,
the next term will be 6569,
the then next term, I'm going to cheat,
and if I start using a calculator,
if I add these up…
10,830…
45,628— I'll do a few of these, and you can zip through, obviously.
BRADY: So is this the Brady sequence?
MATT: This is the Brady sequence! We're going to call these the Brady numbers.
So as we go down, I'm — you've got your very—
Am I the first person who has given you your own numbers?
BRADY: Is this going to get on the Online Encyclopedia— MATT: I find that hard—
MATT: This will be in the Online Encyclopedia of Integer Sequences.
I guarantee you, someone will put the Brady sequence up,
and there's not even a Matt sequence, which I find hugely offensive.
So these are getting big. Should we go until we get just past a million?
Let's do that.
Okay, so let's stop there: 1,325,165.
BRADY: That's the lowest seven-digit Brady number!
MATT: That is the first seven-digit Brady number!
So now we've got this list of the Brady numbers,
Shall we see, I mean the Fibonacci numbers,
they have ϕ (phi) as their ratio,
shall we see what the Brady numbers have?
Okay, so we start with the last one here, 1,325,165…
divided by the one before it, so I'm doing the ratio of these two here,
divided by 818,996…
equals 1.6180359,
and the golden ratio is 1.6180339, and so on, right?
So, the ratio of the Brady numbers,
How many have I done? You started with two…
So let's count those. One, two, three, four, five, six, seven, eight, nine, ten…
…eleven, twelve, thirteen… the fourteenth.
We only got to the fourteenth Brady number,
and look how many decimal places it matches the golden ratio.
It's because,
I mean, I don't want to say it's not because the Brady numbers are special,
because obviously they are,
but on top of that, it works for any sequence.
If you start any sequence where you add the two previous terms to get the next term,
you will always approach the golden ratio.
So it's not just Fibonacci, it's any sequence whatsoever, that you come across,
and we can prove that.
MATT: What letter would you like, Brady? Any Greek letter? Do you have a favorite?
BRADY: Uh… Delta?
MATT: Delta